Question

In: Physics

A brave child decides to grab on to an already spinning merry-go-round. The child is initially...

A brave child decides to grab on to an already spinning merry-go-round. The child is initially at rest and has a mass of 31.5 kg. The child grabs and clings to a bar that is 1.40 m from the center of the merry-go-round, causing the angular velocity of the merry-go-round to abruptly drop from 55.0 rpm to 17.0 rpm. What is the moment of inertia of the merry-go-round with respect to its central axis?

Expert Solution

Law of Conservation Angular Momentum:

The angular momentum of the object does not change with adding or subtracting the mass from the rotating body because this change is immediately accompanied by the change in the rotation rate of the object, therefore, angular momentum remains conserved in an isolated system.

Where;

is Angular velocity and I is Moment of inertia.

Conservation angular momentum:

Sol:

Given data:

m=31.5 kg be the mass of the child

r=1.40 m be the radius of rotation of the child

ωi = 55 rpm be the initial angular velocity of the merry-go-round

ωf=17 rpm be the final angular velocity of the merry-go-round

Here as we know that total angular momentum is always conserved for child + round system.

So, by applying the law of conservation of angular momentum and we can get:

Therefore, the moment of inertia of the merry-go-round with respect to its central axis is 27.6 kgm2.

genius_generous answered 2 years ago

A 4.0 ? diameter merry-go-round (mass 270 ??) is spinning at 15 ???. A child of...

A 4.0 ? diameter merry-go-round (mass 270 ??) is spinning at 15 ???. A child of 35.0 ?? runs tangent to the merry-go-round at 3.0 ?/?, in the same direction that it is turning, and jumps onto the outer edge. Calculate the merry-go-round’s angular velocity, immediately after the child jumps on.

Suppose a child gets off a rotating merry-go-round. Does the angular velocity of the merry-go-round increase,...

Suppose a child gets off a rotating merry-go-round. Does the angular velocity of the merry-go-round increase, decrease, or remain the same if: (a) He jumps off radially? (b) He jumps backward to land motionless? (c) He jumps straight up and hangs onto an overhead tree branch? (d) He jumps off forward, tangential to the edge?

sean is at work spinning on a merry-go-round. since his feet are place at the very...

sean is at work spinning on a merry-go-round. since his feet are place at the very edge, his mom is standing 1 foot away, afraid he might fall. sean's distance, d, from his mom is a sinusoidal function of time. suppose that at 1 second, he passes his mom. four seconds later, he passes her again. the diameter of merry-go-round is 8 feet. a) graph D= f(t), where t is time in seconds. label your axes. b) find a possible...

a. A child is sitting on the outer edge of a merry-go-round that is 3.19 m...

a. A child is sitting on the outer edge of a merry-go-round that is 3.19 m in diameter. If the merry-go-round makes 8.9 rev/min, what is the velocity of the child in m/s? b. A markswoman of mass 73 kg shoots a bullet of mass 96 grams at a muzzle velocity of 696 m/s. What should the recoil speed of the markswoman be, if she is standing on a slick surface? c. A golf ball of mass 0.050 kg has...

A merry-go-round is spinning at a rate of 5 revolutions per minute. Cora is sitting 0.5...

A merry-go-round is spinning at a rate of 5 revolutions per minute. Cora is sitting 0.5 m from the center of the merry-go -round and Cameron is sitting right on the edge, 2.0 m from the center. What is the relationship between rotational speed of the two children? a. Cameron's rotational speed is four times as much as Cora's rotational speed b. Cora's rotational speed is the same as Cameron's rotational speed c. Cora's rotational speed is four times as...

A playground merry-go-round is set spinning at 0.20 rev/s and then released. It slows to rest...

A playground merry-go-round is set spinning at 0.20 rev/s and then released. It slows to rest in 25 s. (a) Find the average angular acceleration of the merry-go-round during this time. (b) Assuming now that the angular acceleration is constant, how many turns does it make as it comes to rest?

A child of mass 50 kg is standing at the edge of a playground merry-go-round of...

A child of mass 50 kg is standing at the edge of a playground merry-go-round of diameter 3 m. Other children push the merry-go-round faster and faster until the first child's feet begin to slip. (a) If the coefficient of friction between the shoes and the rotating surface is 0.2, how long does it take the merry-go-round to make one revolution? (b) How fast is the first child traveling when he begins to slip? (c) What is the angle between...

Consider the child's playground merry-go-round wheel. Merry Go Round If the steel disk has mass of...

Consider the child's playground merry-go-round wheel. Merry Go Round If the steel disk has mass of 200 kg and a radius of 2 meters you can make it spin by applying a force to the rim. This torque increases the angular momentum of the disk. Suppose the force is 20 newtons. How long would you have to apply it to get the wheel spinning 5 times a minute? What would happen to the rate of spin if you then jumped...

A 25.25 kg child is riding a playground merry-go-round that is rotating at 35.5 rev/min. (A)...

A 25.25 kg child is riding a playground merry-go-round that is rotating at 35.5 rev/min. (A) What net force is acting on her if she is standing on the merry-go-round 1.4 m from its center in newtons? The net force in this situation is sometimes called "centripetal force". (B) What net force (in N) is acting on her if she is standing on an amusement park merry-go-round that rotates at 3.2 rpm and she is 7.6 m from its center?...

A 50.0 kg child stands at the rim of a merry-go-round of radius 1.50 m, rotating...

A 50.0 kg child stands at the rim of a merry-go-round of radius 1.50 m, rotating with an angular speed of 2.50 rad/s. (a) What is the child's centripetal acceleration? m/s2 (b) What is the minimum force between her feet and the floor of the merry-go-round that is required to keep her in the circular path? N (c) What minimum coefficient of static friction is required? Is the answer you found reasonable? In other words, is she likely to be...